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Thread: Proving an Inequality

  1. June 1st 2010, 06:51 AM #1
    GIPC
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    Proving an Inequality

    I was thinking of using convex function properties to prove the following inequality but couldn't. I'm not sure what else should I use.

    1-(a/b)<ln(b/a)<(b/a) -1
    given that 0<a<b
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  2. June 1st 2010, 07:08 AM #2
    Plato
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    Quote Originally Posted by GIPC View Post
    1-(a/b)<ln(b/a)<(b/a) -1
    given that 0<a<b
    Use the mean value theorem to prove Napier's inequality:
    \frac{1}{b}\le\frac{\log(b)-\log(a)}{b-a}\le\frac{1}{a}.
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